InterviewSolution
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InterviewSolution
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Explain the kinetic interpretation of Temperature. |
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Answer» Solution :According to kinetic theory of gases, the pressure P exerted by one mole of an ideal gas is given by `P = 1/3 rhoC^(2) implies P = 1/3 M/V C^(2)` `( :. "density" , rho = M/V)` `implies PV = 1/3 MC^(2)` But `PV = RT` `:. C^(2) = (3RT)/(M) or C^(2) prop T implies C prop sqrt(T)` or `sqrt(T) prop C` where C is RMS velocity eof gas . Thus, the SQUARE root of the absolute termperature of an idea gas is DIRECTLY proportional to root mean square velocity or its molecules. ALSO, from eqn. (1) `1/3 M/(N_A) C^(2) = R/(N_A) T = k_(B)T implies 1/2 mc^(2) = 3/2 k_(B)T` `implies 1/2 mc^(2) prop T( :. 3/2 k_(B)` is CONSTANT) But , `1/2 mc^(2)` is average translational K.E. per molecule of a gas. Therefore, average kinetic energy of translation per molecule of a gas is directly proportional to the absolute temperature of the gas. |
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